Improvement of the method for analysis of nonlinear electrotechnical systems based on the small parameter method - Maliakova, Mariia (Eastern-European Journal of Enterprise Technologies, 2018)
The small parameter method, implemented in frequency domain, was used for the analytical analysis of nonlinear electrical circuits of electrotechnical systems. To have the possibility of calculations in frequency domain, the automated method of forming orthogonal harmonic components of electrical magnitudes based on the algorithm of discrete convolution was used. The characteristic of a nonlinear element was represented by the polynomial function of third degree. It was shown that application of the small parameter method with its realization in frequency domain makes it possible to simplify the process of analyzing electrical circuits with nonlinear elements by automating calculations in the mathematical package. Analytical and numerical calculations of a circuit with actively inductive load demonstrated sufficient accuracy of the proposed method, the relative error for the main harmonic of current did not exceed 6 %. The conducted comparative analysis of the proposed small parameter method with the classic small parameter method on the example of calculation of an electrical circuit with RL load showed that the developed method provides better adequacy of results and high calculation accuracy in comparison with the existing one. Relative error by amplitude of first and third harmonics of current does not exceed 2.5 %, and by phase, it does not exceed 1.042·10-3 %. The method of numerical structural modeling was used to determine the reference values of current of the researched circuit. The results of the research can be used in calculations of electrotechnical devices, containing semiconductor components and electrical devices with nonlinear characteristics. In addition, the obtained results will make it possible to improve the processes of active compensation of harmonics of current in electrical networks with nonlinear load and to develop the tools of passive compensation